In digital communications systems, a carrier signal is modulated with the digital data to be transmitted over the channel, where it typically suffers various forms of distortion, such as additive noise. The digital data is often transmitted in bursts wherein each burst consists of a number of data bits. Upon reception, the signal must be demodulated in order to recover the transmitted data.
It is common for receivers to employ direct conversion (i.e. homodyne receiver) to perform the demodulation of the received signal. The received signal is mixed with a local oscillator signal at the carrier frequency to produce I (in-phase) and Q (quadrature) baseband signals. An advantage of direct conversion receivers is that they are efficient in terms of cost and current consumption. The advantage is derived from having the incoming RF signal directly downconverted to baseband, in both I and Q components, without use of any IF frequencies.
In other receivers, the incoming RF signal is mixed down first to an intermediate frequency (IF) signal and subsequently to baseband. The IF frequency may be any convenient frequency. For example, in a Bluetooth receiver, the front-end may output a low frequency IF signal (e.g., Near-Zero IF, which is 0.5 MHz, since the signal's bandwidth is 1 MHz).
One of the errors commonly introduced into the signal is frequency offsets. The errors may be introduced at both the transmitter and the receiver. An example baseband signal that is recovered in the absence of frequency offsets is shown in FIG. 1A. The FSK baseband signal 40 is a filtered baseband signal filtered with a Gaussian filter in accordance with the Bluetooth specifications. The baseband signal is recovered by the detector and is ready for further processing including slicing, equalization, etc. Note that the frequency deviations representing the ‘0’ and ‘2’ symbols are centered around zero and extend to ±Rbh=±160 kHz where h is the modulation index (e.g., 0.32) and Rb is the data rate (e.g., 1 Msps). The output signal which is recovered in the presence of frequency offsets is as shown in FIG. 1B.
Note that in the example embodiment presented here, fixed frequency offsets translate to a constant DC level at the output of the demodulator. The frequency offsets, however, are not always constant and may vary over time. The variations in frequency offset translate to variations in the DC level, such as the slowly decaying DC level shown in FIG. 1B, corresponding to a frequency droop in the received signal (the Bluetooth specifications allow as much as ±40 kHz of frequency droop in a long packet). The signal 42 rides on a DC or near DC (low frequency) signal with a range defined by the maximum peaks 44 and minimum peaks 46. Depending on the type of detector used, frequency offsets could be translated into either DC offsets, which may be fixed or vary at a low rate, or into other distortions on the recovered signal which would typically be more difficult to eliminate.
Considering FSK modulation without any frequency offset errors, the signal output from the transmitter can be expressed mathematically by the following.I=A cos(ωct+φ(t)+θ)  (1)where A is a constant, ωc represents the carrier signal, φ(t) represents the data and θ represents random noise. I is the signal after downconversion from RF to IF wherein the local oscillator frequency is given by LO=ωC−ωIF where ωIF denotes the IF frequency, which is 500 kHz in a Near-Zero IF Bluetooth receiver. The downconverted signal is expressed mathematically as follows.I=A cos(ωIFt+φ(t)+θ)  (2)After downconversion from IF to zero-IF, the output signal is given byI=A cos(φ(t)+θ)  (3)Differential detection of this signal calculates(φ(t)+θ(t))−(φ(t−T)+θ(t−T))Δφ  (4)where T represents the symbol time. In Bluetooth systems, the symbol time T is 1 microsecond. The result of differential detection yields sin(Δφ), which for small values of φ can be approximated as simply Δφ.
In the real world, however, frequency offsets are introduced causing distortion of the received signal. Considering a communication system constructed in accordance with the Bluetooth standard, the receiver must be constructed to deal with frequency offsets in order to generate a reliable output signal (i.e. minimize the number of erroneous bits in the recovered data). There exist several sources of frequency offset errors in a Bluetooth communication system as highlighted below.
First, the Bluetooth specification permits a frequency error of up to 75 kHz in carrier frequency of the transmitted signal. Second, an additional frequency offset of up to 50 kHz may be added by the receiver's local-oscillator as a result of up to 20 ppm of frequency error that its crystal reference may have. Further, a third contributor of up to 40 kHz of frequency drift may be resulting from the frequency droop allowed by the Bluetooth specifications for packets occupying 3-5 time slots. Lastly, a fourth contributor of up to 15 kHz of frequency error may be resulting from frequency variations in the receiver clocks as a result of them being derived from the frequency-hopping RF signal (in a specific implementation). This last contributor could be avoided by using accurate fixed clocks rather than division of the frequency-varying RF signal at the output of the LO frequency synthesizer.
Thus, an input signal may have a total of ±180 kHz in frequency offset. Considering a peak frequency deviation of +/−160 kHz for a modulation index of 0.32, a possible frequency offset of 180 kHz makes reception virtually impossible. Note that using a modulation index of 0.28, which is allowed by the Bluetooth specifications, resulting in only 140 kHz of peak frequency deviation, makes the problem even worse.
If the frequency offset is represented by ΔωIF, the expression for the downconversion to IF is as follows.I=A cos((ωIF+ΔωIF)t+φ(t)+φ)  (5)After the second downconversion to zero-IF, the output can be expressed asI=A cos(ΔωIF(t)+φ(t)+θ)  (6)Differential detection of this signal yields sin(Δφ+ΔωIFT) which is the baseband signal corrupted by frequency offset errors. The second term represents a phase added to the signal caused by the frequency offset. Thus, in a symbol time of 1 microsecond, a frequency offset of 180 kHz yields a phase error of 0.36π radians. Considering a phasor representation of the FSK signal, the frequency offset causes the rotation to speed up or slow down to the point where the received signal cannot be distinguished from the frequency offset thus preventing proper reception of the received signal.
Prior art frequency offset compensation schemes are typically based on closed loop solutions in which the frequency of a local oscillator used for downconversion is adjusted. In a receiver implemented digitally, involving a second downconversion stage, frequency offset correction circuits are typically implemented using a numerically controlled oscillator (NCO) in some form of closed loop feedback arrangement whereby feedback control of the NCO must be synchronized with the detected frequency offset. This solution is difficult in a receiver with multistage processing latency delays along the path and is also unattractive in terms of complexity and therefore size, cost and current consumption. Due to the long delay loop, stabilization is problematic and in addition, it is too late to apply the correction to the data that has already been downconverted and stored in various buffers in the receiver processing stages.
In other prior art solutions, the frequency offset is translated to a phase shift in the constellation of the received signal. The phase shift is typically removed utilizing various complex digital signal processing techniques.
Thus a reduced-complexity mechanism is needed that is able to maintain a target BER<0.1% performance at −85 dBm (a typical sensitivity level specified for the receiver) despite the frequency offsets which may be present, potentially exceeding the frequency deviations of the modulation itself.